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java.lang.Objectpapaya.Gamma
public class Gamma
Gamma and Beta functions.
Implementation:
The code is mostly adapted from the CERN
Jet Java libraries, which in turn was adapted from the Cephes Mathematical Library. As far a
as I can tell, Stephen L. Moshier wrote the original C++ code for CEPHES (1989, moshier@na-net.ornl.gov)
and Wolfgang Hoschek (at CERN, hats off to you mate!) then adapted it for the
Java platform, making some significant changes along the way.
Field Summary |
---|
Fields inherited from interface papaya.PapayaConstants |
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BASELINE, big, biginv, BOTTOM, CENTER, CORNER, FONTNAME, GRAY, INDEX_NOT_FOUND, INDICES_NOT_FOUND, LEFT, LOGPI, MACHEP, MAXGAM, MAXLOG, MINLOG, RIGHT, SQRTH, SQTPI, STROKEWEIGHT, TEXTSIZE, TOP |
Method Summary | |
---|---|
static float |
beta(double a,
double b)
Returns the beta function of the arguments. |
static double |
gamma(double x)
Returns the Gamma function of the argument, Γ(x) |
static double |
incompleteBeta(double aa,
double bb,
double xx)
Returns the Incomplete Beta Function evaluated from zero to xx ; formerly named ibeta . |
static double |
incompleteBetaInverse(double aa,
double bb,
double yy0)
Returns the inverse of the incomplete Beta integral. |
static double |
incompleteGamma(double a,
double x)
Returns the Incomplete Gamma function; formerly named igamma . |
static double |
incompleteGammaComplement(double a,
double x)
Returns the Complemented Incomplete Gamma function; formerly named igamc. |
static double |
logGamma(double x)
Returns the natural logarithm of the gamma function; formerly named lgamma . |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Method Detail |
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public static float beta(double a, double b) throws ArithmeticException
beta( a, b ) = Γ(a) * Γ(b) ) Γ(a+b)
ArithmeticException
public static double gamma(double x) throws ArithmeticException
Γ(x)
ArithmeticException
public static double incompleteBeta(double aa, double bb, double xx) throws ArithmeticException
xx
; formerly named ibeta
.
aa
- the alpha parameter of the beta distribution.bb
- the beta parameter of the beta distribution.xx
- the integration end point.
ArithmeticException
public static double incompleteBetaInverse(double aa, double bb, double yy0)
y
, the function finds x
such that
incompleteBeta( a, b, x ) = y.The routine performs interval halving until
incompleteBeta(a,b,x) - y = 0
,
to within roughly 10^-13
of the true solution. If this precision is not reached, the
method returns the current approximation of x, and prints a warning statement
specifying the current error. Typically, this is on the order of 10^-12.
aa
- the alpha parameter of the beta distribution.bb
- the beta parameter of the beta distribution.yy0
- the value for which to solve for the corresponding x
in the
incomplete Beta integral.
x
such that incompleteBeta( a, b, x ) = y
.public static double incompleteGamma(double a, double x) throws ArithmeticException
igamma
.
a
- the parameter of the gamma distribution.x
- the integration end point.
ArithmeticException
public static double incompleteGammaComplement(double a, double x) throws ArithmeticException
a
- the parameter of the gamma distribution.x
- the integration start point.
ArithmeticException
public static double logGamma(double x) throws ArithmeticException
lgamma
.
ArithmeticException
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